Short proof of Sobczyk’s theorem
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- by William A. Veech PDF
- Proc. Amer. Math. Soc. 28 (1971), 627-628 Request permission
Abstract:
A new proof is given of Sobczyk’s Theorem, which asserts that ${c_0}$ is complemented in any separable Banach space which contains it (isomorphically) as a closed subspace.References
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Andrew Sobczyk, Projection of the space $(m)$ on its subspace $(c_0)$, Bull. Amer. Math. Soc. 47 (1941), 938–947. MR 5777, DOI 10.1090/S0002-9904-1941-07593-2
- Gottfried Köthe, Über einen Satz von Sobczyk, An. Fac. Ci. Univ. Porto 49 (1966), 281–286 (German). MR 0227738
- Seymour Goldberg, On Sobczyk’s projection theorem, Amer. Math. Monthly 76 (1969), 523–526. MR 244740, DOI 10.2307/2316961
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 627-628
- MSC: Primary 46.10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0275122-0
- MathSciNet review: 0275122